On the Magnetospheric Beat-frequency and Lense-thirring Interpretations of the Horizontal-branch Oscillation in the Z Sources

Three types of quasi-periodic oscillations (QPOs) have been discovered so far in the persistent emission of the most luminous neutron star low-mass X-ray binaries, the Z sources : D10È60 Hz horizontalbranch and D6È20 Hz normal/Ñaring-branch oscillations and D200È1200 Hz kilohertz QPOs, which usually occur in pairs. Here we study the horizontal-branch oscillations and the two simultaneous kilohertz QPOs, which were discovered using the Rossi X-Ray T iming Explorer, comparing their properties in Ðve Z sources with the predictions of the magnetospheric beat-frequency and Lense-Thirring precession models. We Ðnd that the variation of the horizontal-branch oscillation frequency with accretion rate predicted by the magnetospheric beat-frequency model for a purely dipolar stellar magnetic Ðeld and a radiation-pressureÈdominated inner accretion disk is consistent with the observed variation. The model predicts a universal relation between the horizontal-branch oscillation, stellar spin, and upper kilohertz QPO frequencies that agrees with the data on Ðve Z sources. The model implies that the neutron stars in the Z sources are near magnetic spin equilibrium, that their magnetic Ðeld strengths are D109È1010 G, and that the critical fastness parameter for these sources is If the frequency of the upper kiloZ0.8. hertz QPO is an orbital frequency in the accretion disk, the magnetospheric beat-frequency model requires that a small fraction of the gas in the disk does not couple strongly to the stellar magnetic Ðeld at 3È4 stellar radii but instead drifts slowly inward in nearly circular orbits until it is within a few kilometers of the neutron star surface. The Lense-Thirring precession model is consistent with the observed magnitudes of the horizontal-branch oscillation frequencies only if the moments of inertia of the neutron stars in the Z sources are D4È5 times larger than the largest values predicted by realistic neutron star equations of state. If instead the moments of inertia of neutron stars have the size expected and their spin frequencies in the Z sources are approximately equal to the frequency separation of the kilohertz QPOs, Lense-Thirring precession can account for the magnitudes of the horizontal-branch oscillation frequencies only if the fundamental frequency of the horizontal-branch oscillation is at least 4 times the precession frequency. We argue that the change in the slope of the correlation between the frequency of the horizontal-branch oscillation and the frequency of the upper kilohertz QPO, when the latter is greater than 850 Hz, is directly related to the varying frequency separation of the kilohertz QPOs. Subject headings : accretion, accretion disks È binaries : close È X-rays : stars